Coupled Coincidence Point Theorems In Several Spaces

In 2006, Bhashar and Lakshmikantham introduced the concept of mixed monotone property, in partially ordered metric spaces, and proved some coupled fixed point theorems.Afterwards, Sintunavarat et al. did a further research, and weakened the mixed monotone property of F by introducing F-invarent set, having some corresponding coupled fixed point results. In this paper, we present the new definition of F- g-invarent set with the help of mixed g-monotone property of F due to Lakshmikantham and Ciric in 2009, and obtain some coupled coincidence point theorems. Presented theorems have generated results of corresponding literatures. The paper mainly divided three chapters.The first chapter is introduction, and it mainly introduce the relevant problems with respect to coupled fixed and coincidence point, moreover, it also list the necessary definitions,lemmas and theorems which will be needed in the sequel.The second chapter weaken the mixed g-monotone property of mapping F by introducing the concept of F- g-invarint set in separable metric spaces, and obtain some coupled coincidence point theorems.The third chapter omit the commutativity of mappings F and g in cone metric spaces with c- distance, and weaken the mixed g-monotone property of mapping F by introducing the concept of F- g-invarint set, having some meaningful results.